There’s both an imperial and a metric ”0603” package… The metric one is 0,6×0,3 mm² (very, very tiny), the imperial one is 60×30 mil² = 0,06″×0,03″ = 1,6mm × 0,8mm. But I think generally people mean the imperial sizes when they talk about, e.g. a “0805 resistor”.

I wouldn’t really trust any standard “thickness” with SMD caps, I’ve seen a few surprisingly tall ones.

vogelchr said it best — there’s both the metric and imperial. After years of working with smd components I just learned that the 0603 actually specifies the dimensions after looking up a size chart for them. I could believe I missed such an obvious thing for so long! Still, capacitors do vary a lot within 0603, unlike resistors.